Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3

Percentage Accurate: 88.1% → 99.5%

Time: 7.2s

Alternatives: 16

Speedup: 0.8×

• 21.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * ((y - z) + 1.0d0)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}

Python

def code(x, y, z):
	return (x * ((y - z) + 1.0)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * ((y - z) + 1.0)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Initial Program: 88.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))

C

double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * ((y - z) + 1.0d0)) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}

Python

def code(x, y, z):
	return (x * ((y - z) + 1.0)) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(Float64(y - z) + 1.0)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * ((y - z) + 1.0)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + \left(y - z\right)}}\\ \mathbf{elif}\;z \leq 0.00135:\\ \;\;\;\;\frac{x + x \cdot \left(y - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.55e+23)
   (/ x (/ z (+ 1.0 (- y z))))
   (if (<= z 0.00135) (/ (+ x (* x (- y z))) z) (- (* x (/ y z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.55e+23) {
		tmp = x / (z / (1.0 + (y - z)));
	} else if (z <= 0.00135) {
		tmp = (x + (x * (y - z))) / z;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.55d+23)) then
        tmp = x / (z / (1.0d0 + (y - z)))
    else if (z <= 0.00135d0) then
        tmp = (x + (x * (y - z))) / z
    else
        tmp = (x * (y / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.55e+23) {
		tmp = x / (z / (1.0 + (y - z)));
	} else if (z <= 0.00135) {
		tmp = (x + (x * (y - z))) / z;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.55e+23:
		tmp = x / (z / (1.0 + (y - z)))
	elif z <= 0.00135:
		tmp = (x + (x * (y - z))) / z
	else:
		tmp = (x * (y / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.55e+23)
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(y - z))));
	elseif (z <= 0.00135)
		tmp = Float64(Float64(x + Float64(x * Float64(y - z))) / z);
	else
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.55e+23)
		tmp = x / (z / (1.0 + (y - z)));
	elseif (z <= 0.00135)
		tmp = (x + (x * (y - z))) / z;
	else
		tmp = (x * (y / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.55e+23], N[(x / N[(z / N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00135], N[(N[(x + N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5500000000000001e23

   1. Initial program 80.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 80.6%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. *-rgt-identity 80.6%

         \[\leadsto \frac{x \cdot \left(y - z\right) + \color{blue}{x}}{z} \]

   3. Applied egg-rr 80.6%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x}}{z} \]

   4. Taylor expanded in x around 0 80.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(\left(1 + y\right) - z\right)}{z}} \]
   5. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(1 + y\right) - z}}} \]

      2. associate--l+ 99.9%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{1 + \left(y - z\right)}}} \]

   6. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{1 + \left(y - z\right)}}} \]

   if -2.5500000000000001e23 < z < 0.0013500000000000001

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 99.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. *-rgt-identity 99.9%

         \[\leadsto \frac{x \cdot \left(y - z\right) + \color{blue}{x}}{z} \]

   3. Applied egg-rr 99.9%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x}}{z} \]

   if 0.0013500000000000001 < z

   1. Initial program 78.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 88.3%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 88.3%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 94.0%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 94.0%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 94.0%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \cdot y \]

      2. +-commutative 94.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y + \left(-x\right)} \]

      3. unsub-neg 94.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y - x} \]

      4. frac-2neg 94.0%

         \[\leadsto \color{blue}{\frac{-x}{-z}} \cdot y - x \]

      5. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{-x}{\frac{-z}{y}}} - x \]

      6. div-inv 99.8%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{\frac{-z}{y}}} - x \]

      7. add-sqr-sqrt 44.7%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      8. sqrt-unprod 60.1%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      9. sqr-neg 60.1%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      10. sqrt-unprod 36.0%

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      11. add-sqr-sqrt 61.4%

          \[\leadsto \color{blue}{x} \cdot \frac{1}{\frac{-z}{y}} - x \]

      12. clear-num 61.4%

          \[\leadsto x \cdot \color{blue}{\frac{y}{-z}} - x \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} - x \]

      14. sqrt-unprod 86.1%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} - x \]

      15. sqr-neg 86.1%

          \[\leadsto x \cdot \frac{y}{\sqrt{\color{blue}{z \cdot z}}} - x \]

      16. sqrt-unprod 99.8%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} - x \]

      17. add-sqr-sqrt 99.9%

          \[\leadsto x \cdot \frac{y}{\color{blue}{z}} - x \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + \left(y - z\right)}}\\ \mathbf{elif}\;z \leq 0.00135:\\ \;\;\;\;\frac{x + x \cdot \left(y - z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \]

Alternative 2: 58.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7.1 \cdot 10^{-62}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-209}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-138}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 420000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (/ y z))))
   (if (<= y -1.25e+26)
     t_0
     (if (<= y -7.1e-62)
       (- x)
       (if (<= y -5.5e-191)
         (/ x z)
         (if (<= y 2.1e-209)
           (- x)
           (if (<= y 1.45e-186)
             (/ x z)
             (if (<= y 1.2e-138)
               (- x)
               (if (<= y 420000000.0) (/ x z) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (y <= -1.25e+26) {
		tmp = t_0;
	} else if (y <= -7.1e-62) {
		tmp = -x;
	} else if (y <= -5.5e-191) {
		tmp = x / z;
	} else if (y <= 2.1e-209) {
		tmp = -x;
	} else if (y <= 1.45e-186) {
		tmp = x / z;
	} else if (y <= 1.2e-138) {
		tmp = -x;
	} else if (y <= 420000000.0) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (y / z)
    if (y <= (-1.25d+26)) then
        tmp = t_0
    else if (y <= (-7.1d-62)) then
        tmp = -x
    else if (y <= (-5.5d-191)) then
        tmp = x / z
    else if (y <= 2.1d-209) then
        tmp = -x
    else if (y <= 1.45d-186) then
        tmp = x / z
    else if (y <= 1.2d-138) then
        tmp = -x
    else if (y <= 420000000.0d0) then
        tmp = x / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y / z);
	double tmp;
	if (y <= -1.25e+26) {
		tmp = t_0;
	} else if (y <= -7.1e-62) {
		tmp = -x;
	} else if (y <= -5.5e-191) {
		tmp = x / z;
	} else if (y <= 2.1e-209) {
		tmp = -x;
	} else if (y <= 1.45e-186) {
		tmp = x / z;
	} else if (y <= 1.2e-138) {
		tmp = -x;
	} else if (y <= 420000000.0) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y / z)
	tmp = 0
	if y <= -1.25e+26:
		tmp = t_0
	elif y <= -7.1e-62:
		tmp = -x
	elif y <= -5.5e-191:
		tmp = x / z
	elif y <= 2.1e-209:
		tmp = -x
	elif y <= 1.45e-186:
		tmp = x / z
	elif y <= 1.2e-138:
		tmp = -x
	elif y <= 420000000.0:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y / z))
	tmp = 0.0
	if (y <= -1.25e+26)
		tmp = t_0;
	elseif (y <= -7.1e-62)
		tmp = Float64(-x);
	elseif (y <= -5.5e-191)
		tmp = Float64(x / z);
	elseif (y <= 2.1e-209)
		tmp = Float64(-x);
	elseif (y <= 1.45e-186)
		tmp = Float64(x / z);
	elseif (y <= 1.2e-138)
		tmp = Float64(-x);
	elseif (y <= 420000000.0)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y / z);
	tmp = 0.0;
	if (y <= -1.25e+26)
		tmp = t_0;
	elseif (y <= -7.1e-62)
		tmp = -x;
	elseif (y <= -5.5e-191)
		tmp = x / z;
	elseif (y <= 2.1e-209)
		tmp = -x;
	elseif (y <= 1.45e-186)
		tmp = x / z;
	elseif (y <= 1.2e-138)
		tmp = -x;
	elseif (y <= 420000000.0)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+26], t$95$0, If[LessEqual[y, -7.1e-62], (-x), If[LessEqual[y, -5.5e-191], N[(x / z), $MachinePrecision], If[LessEqual[y, 2.1e-209], (-x), If[LessEqual[y, 1.45e-186], N[(x / z), $MachinePrecision], If[LessEqual[y, 1.2e-138], (-x), If[LessEqual[y, 420000000.0], N[(x / z), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e26 or 4.2e8 < y

   1. Initial program 90.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 90.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. *-rgt-identity 90.9%

         \[\leadsto \frac{x \cdot \left(y - z\right) + \color{blue}{x}}{z} \]

   3. Applied egg-rr 90.9%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x}}{z} \]

   4. Taylor expanded in y around inf 77.5%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 71.4%

         \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   6. Simplified 71.4%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}} \]

   if -1.25e26 < y < -7.1000000000000001e-62 or -5.5000000000000001e-191 < y < 2.09999999999999996e-209 or 1.4500000000000001e-186 < y < 1.2e-138

   1. Initial program 87.2%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around inf 67.1%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. neg-mul-1 67.1%

         \[\leadsto \color{blue}{-x} \]

   4. Simplified 67.1%

      \[\leadsto \color{blue}{-x} \]

   if -7.1000000000000001e-62 < y < -5.5000000000000001e-191 or 2.09999999999999996e-209 < y < 1.4500000000000001e-186 or 1.2e-138 < y < 4.2e8

   1. Initial program 96.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 96.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. fma-def 96.5%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y - z, x \cdot 1\right)}}{z} \]

      3. *-rgt-identity 96.5%

         \[\leadsto \frac{\mathsf{fma}\left(x, y - z, \color{blue}{x}\right)}{z} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}} \]

   4. Taylor expanded in z around 0 71.2%

      \[\leadsto \color{blue}{\frac{x + x \cdot y}{z}} \]

   5. Taylor expanded in x around -inf 71.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot y - 1\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 71.2%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(-1 \cdot y - 1\right)}{z}} \]

      2. associate-/l* 71.2%

         \[\leadsto -\color{blue}{\frac{x}{\frac{z}{-1 \cdot y - 1}}} \]

      3. distribute-neg-frac 71.2%

         \[\leadsto \color{blue}{\frac{-x}{\frac{z}{-1 \cdot y - 1}}} \]

      4. sub-neg 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{-1 \cdot y + \left(-1\right)}}} \]

      5. neg-mul-1 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{\left(-y\right)} + \left(-1\right)}} \]

      6. metadata-eval 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\left(-y\right) + \color{blue}{-1}}} \]

      7. +-commutative 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{-1 + \left(-y\right)}}} \]

      8. unsub-neg 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{-1 - y}}} \]

   7. Simplified 71.2%

      \[\leadsto \color{blue}{\frac{-x}{\frac{z}{-1 - y}}} \]

   8. Taylor expanded in y around 0 71.0%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -7.1 \cdot 10^{-62}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-209}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-138}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 420000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 61.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-62}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-209}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-138}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 420000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -1.08e+18)
     t_0
     (if (<= y -8.5e-62)
       (- x)
       (if (<= y -5.6e-191)
         (/ x z)
         (if (<= y 3.2e-209)
           (- x)
           (if (<= y 8e-187)
             (/ x z)
             (if (<= y 1.02e-138)
               (- x)
               (if (<= y 420000000.0) (/ x z) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -1.08e+18) {
		tmp = t_0;
	} else if (y <= -8.5e-62) {
		tmp = -x;
	} else if (y <= -5.6e-191) {
		tmp = x / z;
	} else if (y <= 3.2e-209) {
		tmp = -x;
	} else if (y <= 8e-187) {
		tmp = x / z;
	} else if (y <= 1.02e-138) {
		tmp = -x;
	} else if (y <= 420000000.0) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (y <= (-1.08d+18)) then
        tmp = t_0
    else if (y <= (-8.5d-62)) then
        tmp = -x
    else if (y <= (-5.6d-191)) then
        tmp = x / z
    else if (y <= 3.2d-209) then
        tmp = -x
    else if (y <= 8d-187) then
        tmp = x / z
    else if (y <= 1.02d-138) then
        tmp = -x
    else if (y <= 420000000.0d0) then
        tmp = x / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -1.08e+18) {
		tmp = t_0;
	} else if (y <= -8.5e-62) {
		tmp = -x;
	} else if (y <= -5.6e-191) {
		tmp = x / z;
	} else if (y <= 3.2e-209) {
		tmp = -x;
	} else if (y <= 8e-187) {
		tmp = x / z;
	} else if (y <= 1.02e-138) {
		tmp = -x;
	} else if (y <= 420000000.0) {
		tmp = x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -1.08e+18:
		tmp = t_0
	elif y <= -8.5e-62:
		tmp = -x
	elif y <= -5.6e-191:
		tmp = x / z
	elif y <= 3.2e-209:
		tmp = -x
	elif y <= 8e-187:
		tmp = x / z
	elif y <= 1.02e-138:
		tmp = -x
	elif y <= 420000000.0:
		tmp = x / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -1.08e+18)
		tmp = t_0;
	elseif (y <= -8.5e-62)
		tmp = Float64(-x);
	elseif (y <= -5.6e-191)
		tmp = Float64(x / z);
	elseif (y <= 3.2e-209)
		tmp = Float64(-x);
	elseif (y <= 8e-187)
		tmp = Float64(x / z);
	elseif (y <= 1.02e-138)
		tmp = Float64(-x);
	elseif (y <= 420000000.0)
		tmp = Float64(x / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (y <= -1.08e+18)
		tmp = t_0;
	elseif (y <= -8.5e-62)
		tmp = -x;
	elseif (y <= -5.6e-191)
		tmp = x / z;
	elseif (y <= 3.2e-209)
		tmp = -x;
	elseif (y <= 8e-187)
		tmp = x / z;
	elseif (y <= 1.02e-138)
		tmp = -x;
	elseif (y <= 420000000.0)
		tmp = x / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.08e+18], t$95$0, If[LessEqual[y, -8.5e-62], (-x), If[LessEqual[y, -5.6e-191], N[(x / z), $MachinePrecision], If[LessEqual[y, 3.2e-209], (-x), If[LessEqual[y, 8e-187], N[(x / z), $MachinePrecision], If[LessEqual[y, 1.02e-138], (-x), If[LessEqual[y, 420000000.0], N[(x / z), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08e18 or 4.2e8 < y

   1. Initial program 90.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in y around inf 77.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   3. Step-by-step derivation

      1. associate-/l* 72.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

      2. associate-/r/ 77.3%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   4. Simplified 77.3%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   if -1.08e18 < y < -8.4999999999999995e-62 or -5.60000000000000023e-191 < y < 3.2000000000000001e-209 or 8.0000000000000001e-187 < y < 1.02000000000000007e-138

   1. Initial program 88.1%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around inf 67.6%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. neg-mul-1 67.6%

         \[\leadsto \color{blue}{-x} \]

   4. Simplified 67.6%

      \[\leadsto \color{blue}{-x} \]

   if -8.4999999999999995e-62 < y < -5.60000000000000023e-191 or 3.2000000000000001e-209 < y < 8.0000000000000001e-187 or 1.02000000000000007e-138 < y < 4.2e8

   1. Initial program 96.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 96.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. fma-def 96.5%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y - z, x \cdot 1\right)}}{z} \]

      3. *-rgt-identity 96.5%

         \[\leadsto \frac{\mathsf{fma}\left(x, y - z, \color{blue}{x}\right)}{z} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}} \]

   4. Taylor expanded in z around 0 71.2%

      \[\leadsto \color{blue}{\frac{x + x \cdot y}{z}} \]

   5. Taylor expanded in x around -inf 71.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot y - 1\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 71.2%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(-1 \cdot y - 1\right)}{z}} \]

      2. associate-/l* 71.2%

         \[\leadsto -\color{blue}{\frac{x}{\frac{z}{-1 \cdot y - 1}}} \]

      3. distribute-neg-frac 71.2%

         \[\leadsto \color{blue}{\frac{-x}{\frac{z}{-1 \cdot y - 1}}} \]

      4. sub-neg 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{-1 \cdot y + \left(-1\right)}}} \]

      5. neg-mul-1 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{\left(-y\right)} + \left(-1\right)}} \]

      6. metadata-eval 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\left(-y\right) + \color{blue}{-1}}} \]

      7. +-commutative 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{-1 + \left(-y\right)}}} \]

      8. unsub-neg 71.2%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{-1 - y}}} \]

   7. Simplified 71.2%

      \[\leadsto \color{blue}{\frac{-x}{\frac{z}{-1 - y}}} \]

   8. Taylor expanded in y around 0 71.0%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+18}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-62}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-209}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-187}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-138}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 420000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 4: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-19} \lor \neg \left(z \leq 2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{\frac{z}{1 + \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9.5e-19) (not (<= z 2e-31)))
   (/ x (/ z (+ 1.0 (- y z))))
   (/ (+ x (* x y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-19) || !(z <= 2e-31)) {
		tmp = x / (z / (1.0 + (y - z)));
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-9.5d-19)) .or. (.not. (z <= 2d-31))) then
        tmp = x / (z / (1.0d0 + (y - z)))
    else
        tmp = (x + (x * y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9.5e-19) || !(z <= 2e-31)) {
		tmp = x / (z / (1.0 + (y - z)));
	} else {
		tmp = (x + (x * y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9.5e-19) or not (z <= 2e-31):
		tmp = x / (z / (1.0 + (y - z)))
	else:
		tmp = (x + (x * y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9.5e-19) || !(z <= 2e-31))
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(y - z))));
	else
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9.5e-19) || ~((z <= 2e-31)))
		tmp = x / (z / (1.0 + (y - z)));
	else
		tmp = (x + (x * y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9.5e-19], N[Not[LessEqual[z, 2e-31]], $MachinePrecision]], N[(x / N[(z / N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.4999999999999995e-19 or 2e-31 < z

   1. Initial program 82.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 82.5%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. *-rgt-identity 82.5%

         \[\leadsto \frac{x \cdot \left(y - z\right) + \color{blue}{x}}{z} \]

   3. Applied egg-rr 82.5%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x}}{z} \]

   4. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{\frac{x \cdot \left(\left(1 + y\right) - z\right)}{z}} \]
   5. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(1 + y\right) - z}}} \]

      2. associate--l+ 99.8%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{1 + \left(y - z\right)}}} \]

   6. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{1 + \left(y - z\right)}}} \]

   if -9.4999999999999995e-19 < z < 2e-31

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 99.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. fma-def 99.9%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y - z, x \cdot 1\right)}}{z} \]

      3. *-rgt-identity 99.9%

         \[\leadsto \frac{\mathsf{fma}\left(x, y - z, \color{blue}{x}\right)}{z} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}} \]

   4. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{\frac{x + x \cdot y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-19} \lor \neg \left(z \leq 2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{\frac{z}{1 + \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \end{array} \]

Alternative 5: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\left(1 + \left(y - z\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.45e+24)
   (* x (+ -1.0 (/ y z)))
   (if (<= z 2e+15) (* (+ 1.0 (- y z)) (/ x z)) (- (* x (/ y z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.45e+24) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 2e+15) {
		tmp = (1.0 + (y - z)) * (x / z);
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.45d+24)) then
        tmp = x * ((-1.0d0) + (y / z))
    else if (z <= 2d+15) then
        tmp = (1.0d0 + (y - z)) * (x / z)
    else
        tmp = (x * (y / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.45e+24) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 2e+15) {
		tmp = (1.0 + (y - z)) * (x / z);
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.45e+24:
		tmp = x * (-1.0 + (y / z))
	elif z <= 2e+15:
		tmp = (1.0 + (y - z)) * (x / z)
	else:
		tmp = (x * (y / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.45e+24)
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	elseif (z <= 2e+15)
		tmp = Float64(Float64(1.0 + Float64(y - z)) * Float64(x / z));
	else
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.45e+24)
		tmp = x * (-1.0 + (y / z));
	elseif (z <= 2e+15)
		tmp = (1.0 + (y - z)) * (x / z);
	else
		tmp = (x * (y / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.45e+24], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e+15], N[(N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4499999999999999e24

   1. Initial program 80.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 93.9%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 93.9%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 95.4%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 95.4%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   6. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - 1\right)} \]

   if -1.4499999999999999e24 < z < 2e15

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 91.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}} \]

      2. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)} \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \left(\left(y - z\right) + 1\right)} \]

   if 2e15 < z

   1. Initial program 78.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 88.1%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 88.1%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 93.8%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 93.8%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 93.8%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \cdot y \]

      2. +-commutative 93.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y + \left(-x\right)} \]

      3. unsub-neg 93.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y - x} \]

      4. frac-2neg 93.8%

         \[\leadsto \color{blue}{\frac{-x}{-z}} \cdot y - x \]

      5. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{-x}{\frac{-z}{y}}} - x \]

      6. div-inv 99.9%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{\frac{-z}{y}}} - x \]

      7. add-sqr-sqrt 43.5%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      8. sqrt-unprod 59.3%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      9. sqr-neg 59.3%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      10. sqrt-unprod 36.7%

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      11. add-sqr-sqrt 62.7%

          \[\leadsto \color{blue}{x} \cdot \frac{1}{\frac{-z}{y}} - x \]

      12. clear-num 62.7%

          \[\leadsto x \cdot \color{blue}{\frac{y}{-z}} - x \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} - x \]

      14. sqrt-unprod 85.8%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} - x \]

      15. sqr-neg 85.8%

          \[\leadsto x \cdot \frac{y}{\sqrt{\color{blue}{z \cdot z}}} - x \]

      16. sqrt-unprod 99.8%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} - x \]

      17. add-sqr-sqrt 99.9%

          \[\leadsto x \cdot \frac{y}{\color{blue}{z}} - x \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+24}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+15}:\\ \;\;\;\;\left(1 + \left(y - z\right)\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \]

Alternative 6: 99.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \left(y - z\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{\frac{z}{t_0}}\\ \mathbf{elif}\;z \leq 0.00135:\\ \;\;\;\;\frac{x \cdot t_0}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ 1.0 (- y z))))
   (if (<= z -6e+23)
     (/ x (/ z t_0))
     (if (<= z 0.00135) (/ (* x t_0) z) (- (* x (/ y z)) x)))))

C

double code(double x, double y, double z) {
	double t_0 = 1.0 + (y - z);
	double tmp;
	if (z <= -6e+23) {
		tmp = x / (z / t_0);
	} else if (z <= 0.00135) {
		tmp = (x * t_0) / z;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (y - z)
    if (z <= (-6d+23)) then
        tmp = x / (z / t_0)
    else if (z <= 0.00135d0) then
        tmp = (x * t_0) / z
    else
        tmp = (x * (y / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 1.0 + (y - z);
	double tmp;
	if (z <= -6e+23) {
		tmp = x / (z / t_0);
	} else if (z <= 0.00135) {
		tmp = (x * t_0) / z;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 1.0 + (y - z)
	tmp = 0
	if z <= -6e+23:
		tmp = x / (z / t_0)
	elif z <= 0.00135:
		tmp = (x * t_0) / z
	else:
		tmp = (x * (y / z)) - x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(1.0 + Float64(y - z))
	tmp = 0.0
	if (z <= -6e+23)
		tmp = Float64(x / Float64(z / t_0));
	elseif (z <= 0.00135)
		tmp = Float64(Float64(x * t_0) / z);
	else
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 1.0 + (y - z);
	tmp = 0.0;
	if (z <= -6e+23)
		tmp = x / (z / t_0);
	elseif (z <= 0.00135)
		tmp = (x * t_0) / z;
	else
		tmp = (x * (y / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+23], N[(x / N[(z / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00135], N[(N[(x * t$95$0), $MachinePrecision] / z), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.0000000000000002e23

   1. Initial program 80.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 80.6%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. *-rgt-identity 80.6%

         \[\leadsto \frac{x \cdot \left(y - z\right) + \color{blue}{x}}{z} \]

   3. Applied egg-rr 80.6%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x}}{z} \]

   4. Taylor expanded in x around 0 80.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(\left(1 + y\right) - z\right)}{z}} \]
   5. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(1 + y\right) - z}}} \]

      2. associate--l+ 99.9%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{1 + \left(y - z\right)}}} \]

   6. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{1 + \left(y - z\right)}}} \]

   if -6.0000000000000002e23 < z < 0.0013500000000000001

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   if 0.0013500000000000001 < z

   1. Initial program 78.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 88.3%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 88.3%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 94.0%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 94.0%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 94.0%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \cdot y \]

      2. +-commutative 94.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y + \left(-x\right)} \]

      3. unsub-neg 94.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y - x} \]

      4. frac-2neg 94.0%

         \[\leadsto \color{blue}{\frac{-x}{-z}} \cdot y - x \]

      5. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{-x}{\frac{-z}{y}}} - x \]

      6. div-inv 99.8%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{\frac{-z}{y}}} - x \]

      7. add-sqr-sqrt 44.7%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      8. sqrt-unprod 60.1%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      9. sqr-neg 60.1%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      10. sqrt-unprod 36.0%

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      11. add-sqr-sqrt 61.4%

          \[\leadsto \color{blue}{x} \cdot \frac{1}{\frac{-z}{y}} - x \]

      12. clear-num 61.4%

          \[\leadsto x \cdot \color{blue}{\frac{y}{-z}} - x \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} - x \]

      14. sqrt-unprod 86.1%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} - x \]

      15. sqr-neg 86.1%

          \[\leadsto x \cdot \frac{y}{\sqrt{\color{blue}{z \cdot z}}} - x \]

      16. sqrt-unprod 99.8%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} - x \]

      17. add-sqr-sqrt 99.9%

          \[\leadsto x \cdot \frac{y}{\color{blue}{z}} - x \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + \left(y - z\right)}}\\ \mathbf{elif}\;z \leq 0.00135:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \]

Alternative 7: 94.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+17} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.8e+17) (not (<= y 1.0)))
   (* x (+ -1.0 (/ y z)))
   (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+17) || !(y <= 1.0)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.8d+17)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * ((-1.0d0) + (y / z))
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.8e+17) || !(y <= 1.0)) {
		tmp = x * (-1.0 + (y / z));
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.8e+17) or not (y <= 1.0):
		tmp = x * (-1.0 + (y / z))
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.8e+17) || !(y <= 1.0))
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.8e+17) || ~((y <= 1.0)))
		tmp = x * (-1.0 + (y / z));
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.8e+17], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8e17 or 1 < y

   1. Initial program 90.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 92.5%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 92.5%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 95.3%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 95.3%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   6. Taylor expanded in x around 0 88.4%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - 1\right)} \]

   if -3.8e17 < y < 1

   1. Initial program 91.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around 0 98.5%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x}{z}} \]
   4. Step-by-step derivation

      1. neg-mul-1 98.5%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \]

      2. +-commutative 98.5%

         \[\leadsto \color{blue}{\frac{x}{z} + \left(-x\right)} \]

      3. unsub-neg 98.5%

         \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   5. Simplified 98.5%

      \[\leadsto \color{blue}{\frac{x}{z} - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+17} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 8: 94.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+17)
   (- (* x (/ y z)) x)
   (if (<= y 1.0) (- (/ x z) x) (* x (+ -1.0 (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+17) {
		tmp = (x * (y / z)) - x;
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (-1.0 + (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.8d+17)) then
        tmp = (x * (y / z)) - x
    else if (y <= 1.0d0) then
        tmp = (x / z) - x
    else
        tmp = x * ((-1.0d0) + (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+17) {
		tmp = (x * (y / z)) - x;
	} else if (y <= 1.0) {
		tmp = (x / z) - x;
	} else {
		tmp = x * (-1.0 + (y / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e+17:
		tmp = (x * (y / z)) - x
	elif y <= 1.0:
		tmp = (x / z) - x
	else:
		tmp = x * (-1.0 + (y / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+17)
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	elseif (y <= 1.0)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+17)
		tmp = (x * (y / z)) - x;
	elseif (y <= 1.0)
		tmp = (x / z) - x;
	else
		tmp = x * (-1.0 + (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e+17], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[y, 1.0], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8e17

   1. Initial program 90.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 93.4%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 93.4%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 93.4%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 93.4%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 93.4%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \cdot y \]

      2. +-commutative 93.4%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y + \left(-x\right)} \]

      3. unsub-neg 93.4%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y - x} \]

      4. frac-2neg 93.4%

         \[\leadsto \color{blue}{\frac{-x}{-z}} \cdot y - x \]

      5. associate-/r/ 89.2%

         \[\leadsto \color{blue}{\frac{-x}{\frac{-z}{y}}} - x \]

      6. div-inv 87.3%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{\frac{-z}{y}}} - x \]

      7. add-sqr-sqrt 40.4%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      8. sqrt-unprod 39.4%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      9. sqr-neg 39.4%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      10. sqrt-unprod 13.5%

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      11. add-sqr-sqrt 19.4%

          \[\leadsto \color{blue}{x} \cdot \frac{1}{\frac{-z}{y}} - x \]

      12. clear-num 19.4%

          \[\leadsto x \cdot \color{blue}{\frac{y}{-z}} - x \]

      13. add-sqr-sqrt 12.0%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} - x \]

      14. sqrt-unprod 46.9%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} - x \]

      15. sqr-neg 46.9%

          \[\leadsto x \cdot \frac{y}{\sqrt{\color{blue}{z \cdot z}}} - x \]

      16. sqrt-unprod 40.6%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} - x \]

      17. add-sqr-sqrt 87.3%

          \[\leadsto x \cdot \frac{y}{\color{blue}{z}} - x \]

   7. Applied egg-rr 87.3%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x} \]

   if -3.8e17 < y < 1

   1. Initial program 91.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around 0 98.5%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x}{z}} \]
   4. Step-by-step derivation

      1. neg-mul-1 98.5%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \]

      2. +-commutative 98.5%

         \[\leadsto \color{blue}{\frac{x}{z} + \left(-x\right)} \]

      3. unsub-neg 98.5%

         \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   5. Simplified 98.5%

      \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   if 1 < y

   1. Initial program 90.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 91.8%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 91.7%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 97.0%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 97.0%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   6. Taylor expanded in x around 0 89.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \end{array} \]

Alternative 9: 95.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.032:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 0.00135:\\ \;\;\;\;\frac{x}{\frac{z}{1 + y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.032)
   (* x (+ -1.0 (/ y z)))
   (if (<= z 0.00135) (/ x (/ z (+ 1.0 y))) (- (* x (/ y z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.032) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 0.00135) {
		tmp = x / (z / (1.0 + y));
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.032d0)) then
        tmp = x * ((-1.0d0) + (y / z))
    else if (z <= 0.00135d0) then
        tmp = x / (z / (1.0d0 + y))
    else
        tmp = (x * (y / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.032) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 0.00135) {
		tmp = x / (z / (1.0 + y));
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.032:
		tmp = x * (-1.0 + (y / z))
	elif z <= 0.00135:
		tmp = x / (z / (1.0 + y))
	else:
		tmp = (x * (y / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.032)
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	elseif (z <= 0.00135)
		tmp = Float64(x / Float64(z / Float64(1.0 + y)));
	else
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.032)
		tmp = x * (-1.0 + (y / z));
	elseif (z <= 0.00135)
		tmp = x / (z / (1.0 + y));
	else
		tmp = (x * (y / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.032], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00135], N[(x / N[(z / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.032000000000000001

   1. Initial program 82.8%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 94.6%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 91.9%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 93.2%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 93.2%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   6. Taylor expanded in x around 0 97.2%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - 1\right)} \]

   if -0.032000000000000001 < z < 0.0013500000000000001

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 99.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. *-rgt-identity 99.9%

         \[\leadsto \frac{x \cdot \left(y - z\right) + \color{blue}{x}}{z} \]

   3. Applied egg-rr 99.9%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x}}{z} \]

   4. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(\left(1 + y\right) - z\right)}{z}} \]
   5. Step-by-step derivation

      1. associate-/l* 90.9%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(1 + y\right) - z}}} \]

      2. associate--l+ 90.8%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{1 + \left(y - z\right)}}} \]

   6. Simplified 90.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{1 + \left(y - z\right)}}} \]

   7. Taylor expanded in z around 0 98.1%

      \[\leadsto \color{blue}{\frac{x \cdot \left(1 + y\right)}{z}} \]
   8. Step-by-step derivation

      1. associate-/l* 89.1%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{1 + y}}} \]

   9. Simplified 89.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{1 + y}}} \]

   if 0.0013500000000000001 < z

   1. Initial program 78.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 88.3%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 88.3%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 94.0%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 94.0%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 94.0%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \cdot y \]

      2. +-commutative 94.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y + \left(-x\right)} \]

      3. unsub-neg 94.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y - x} \]

      4. frac-2neg 94.0%

         \[\leadsto \color{blue}{\frac{-x}{-z}} \cdot y - x \]

      5. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{-x}{\frac{-z}{y}}} - x \]

      6. div-inv 99.8%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{\frac{-z}{y}}} - x \]

      7. add-sqr-sqrt 44.7%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      8. sqrt-unprod 60.1%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      9. sqr-neg 60.1%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      10. sqrt-unprod 36.0%

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      11. add-sqr-sqrt 61.4%

          \[\leadsto \color{blue}{x} \cdot \frac{1}{\frac{-z}{y}} - x \]

      12. clear-num 61.4%

          \[\leadsto x \cdot \color{blue}{\frac{y}{-z}} - x \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} - x \]

      14. sqrt-unprod 86.1%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} - x \]

      15. sqr-neg 86.1%

          \[\leadsto x \cdot \frac{y}{\sqrt{\color{blue}{z \cdot z}}} - x \]

      16. sqrt-unprod 99.8%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} - x \]

      17. add-sqr-sqrt 99.9%

          \[\leadsto x \cdot \frac{y}{\color{blue}{z}} - x \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.032:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 0.00135:\\ \;\;\;\;\frac{x}{\frac{z}{1 + y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \]

Alternative 10: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 0.00135:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1)
   (* x (+ -1.0 (/ y z)))
   (if (<= z 0.00135) (/ (+ x (* x y)) z) (- (* x (/ y z)) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 0.00135) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.1d0)) then
        tmp = x * ((-1.0d0) + (y / z))
    else if (z <= 0.00135d0) then
        tmp = (x + (x * y)) / z
    else
        tmp = (x * (y / z)) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1) {
		tmp = x * (-1.0 + (y / z));
	} else if (z <= 0.00135) {
		tmp = (x + (x * y)) / z;
	} else {
		tmp = (x * (y / z)) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1:
		tmp = x * (-1.0 + (y / z))
	elif z <= 0.00135:
		tmp = (x + (x * y)) / z
	else:
		tmp = (x * (y / z)) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1)
		tmp = Float64(x * Float64(-1.0 + Float64(y / z)));
	elseif (z <= 0.00135)
		tmp = Float64(Float64(x + Float64(x * y)) / z);
	else
		tmp = Float64(Float64(x * Float64(y / z)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1)
		tmp = x * (-1.0 + (y / z));
	elseif (z <= 0.00135)
		tmp = (x + (x * y)) / z;
	else
		tmp = (x * (y / z)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1], N[(x * N[(-1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00135], N[(N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001

   1. Initial program 82.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 94.5%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 92.8%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 94.2%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 94.2%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   6. Taylor expanded in x around 0 98.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - 1\right)} \]

   if -1.1000000000000001 < z < 0.0013500000000000001

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 99.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. fma-def 99.9%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y - z, x \cdot 1\right)}}{z} \]

      3. *-rgt-identity 99.9%

         \[\leadsto \frac{\mathsf{fma}\left(x, y - z, \color{blue}{x}\right)}{z} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}} \]

   4. Taylor expanded in z around 0 97.5%

      \[\leadsto \color{blue}{\frac{x + x \cdot y}{z}} \]

   if 0.0013500000000000001 < z

   1. Initial program 78.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 88.3%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around inf 88.3%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x \cdot y}{z}} \]
   4. Step-by-step derivation

      1. associate-*l/ 94.0%

         \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]

   5. Simplified 94.0%

      \[\leadsto -1 \cdot x + \color{blue}{\frac{x}{z} \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 94.0%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \cdot y \]

      2. +-commutative 94.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y + \left(-x\right)} \]

      3. unsub-neg 94.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y - x} \]

      4. frac-2neg 94.0%

         \[\leadsto \color{blue}{\frac{-x}{-z}} \cdot y - x \]

      5. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{-x}{\frac{-z}{y}}} - x \]

      6. div-inv 99.8%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \frac{1}{\frac{-z}{y}}} - x \]

      7. add-sqr-sqrt 44.7%

         \[\leadsto \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      8. sqrt-unprod 60.1%

         \[\leadsto \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      9. sqr-neg 60.1%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{\frac{-z}{y}} - x \]

      10. sqrt-unprod 36.0%

          \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{\frac{-z}{y}} - x \]

      11. add-sqr-sqrt 61.4%

          \[\leadsto \color{blue}{x} \cdot \frac{1}{\frac{-z}{y}} - x \]

      12. clear-num 61.4%

          \[\leadsto x \cdot \color{blue}{\frac{y}{-z}} - x \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}} - x \]

      14. sqrt-unprod 86.1%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}} - x \]

      15. sqr-neg 86.1%

          \[\leadsto x \cdot \frac{y}{\sqrt{\color{blue}{z \cdot z}}} - x \]

      16. sqrt-unprod 99.8%

          \[\leadsto x \cdot \frac{y}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} - x \]

      17. add-sqr-sqrt 99.9%

          \[\leadsto x \cdot \frac{y}{\color{blue}{z}} - x \]

   7. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{y}{z} - x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1:\\ \;\;\;\;x \cdot \left(-1 + \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 0.00135:\\ \;\;\;\;\frac{x + x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z} - x\\ \end{array} \]

Alternative 11: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.9 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot \left(1 + y\right)}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + \left(y - z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 2.9e-117) (- (/ (* x (+ 1.0 y)) z) x) (/ x (/ z (+ 1.0 (- y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.9e-117) {
		tmp = ((x * (1.0 + y)) / z) - x;
	} else {
		tmp = x / (z / (1.0 + (y - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 2.9d-117) then
        tmp = ((x * (1.0d0 + y)) / z) - x
    else
        tmp = x / (z / (1.0d0 + (y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.9e-117) {
		tmp = ((x * (1.0 + y)) / z) - x;
	} else {
		tmp = x / (z / (1.0 + (y - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2.9e-117:
		tmp = ((x * (1.0 + y)) / z) - x
	else:
		tmp = x / (z / (1.0 + (y - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.9e-117)
		tmp = Float64(Float64(Float64(x * Float64(1.0 + y)) / z) - x);
	else
		tmp = Float64(x / Float64(z / Float64(1.0 + Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2.9e-117)
		tmp = ((x * (1.0 + y)) / z) - x;
	else
		tmp = x / (z / (1.0 + (y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.9e-117], N[(N[(N[(x * N[(1.0 + y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] - x), $MachinePrecision], N[(x / N[(z / N[(1.0 + N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.9000000000000001e-117

   1. Initial program 95.7%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 98.1%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   if 2.9000000000000001e-117 < x

   1. Initial program 83.0%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 83.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. *-rgt-identity 83.0%

         \[\leadsto \frac{x \cdot \left(y - z\right) + \color{blue}{x}}{z} \]

   3. Applied egg-rr 83.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x}}{z} \]

   4. Taylor expanded in x around 0 83.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(\left(1 + y\right) - z\right)}{z}} \]
   5. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(1 + y\right) - z}}} \]

      2. associate--l+ 99.9%

         \[\leadsto \frac{x}{\frac{z}{\color{blue}{1 + \left(y - z\right)}}} \]

   6. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{1 + \left(y - z\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.9 \cdot 10^{-117}:\\ \;\;\;\;\frac{x \cdot \left(1 + y\right)}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{1 + \left(y - z\right)}}\\ \end{array} \]

Alternative 12: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+18} \lor \neg \left(y \leq 5.1 \cdot 10^{+42}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.8e+18) (not (<= y 5.1e+42))) (* y (/ x z)) (- (/ x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e+18) || !(y <= 5.1e+42)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.8d+18)) .or. (.not. (y <= 5.1d+42))) then
        tmp = y * (x / z)
    else
        tmp = (x / z) - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e+18) || !(y <= 5.1e+42)) {
		tmp = y * (x / z);
	} else {
		tmp = (x / z) - x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.8e+18) or not (y <= 5.1e+42):
		tmp = y * (x / z)
	else:
		tmp = (x / z) - x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.8e+18) || !(y <= 5.1e+42))
		tmp = Float64(y * Float64(x / z));
	else
		tmp = Float64(Float64(x / z) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.8e+18) || ~((y <= 5.1e+42)))
		tmp = y * (x / z);
	else
		tmp = (x / z) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.8e+18], N[Not[LessEqual[y, 5.1e+42]], $MachinePrecision]], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.8e18 or 5.0999999999999999e42 < y

   1. Initial program 90.4%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in y around inf 78.7%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   3. Step-by-step derivation

      1. associate-/l* 74.2%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

      2. associate-/r/ 78.9%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   4. Simplified 78.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   if -2.8e18 < y < 5.0999999999999999e42

   1. Initial program 91.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around 0 96.6%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x}{z}} \]
   4. Step-by-step derivation

      1. neg-mul-1 96.6%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \]

      2. +-commutative 96.6%

         \[\leadsto \color{blue}{\frac{x}{z} + \left(-x\right)} \]

      3. unsub-neg 96.6%

         \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   5. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{z} - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+18} \lor \neg \left(y \leq 5.1 \cdot 10^{+42}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} - x\\ \end{array} \]

Alternative 13: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e+17)
   (/ y (/ z x))
   (if (<= y 4.8e+41) (- (/ x z) x) (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+17) {
		tmp = y / (z / x);
	} else if (y <= 4.8e+41) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8d+17)) then
        tmp = y / (z / x)
    else if (y <= 4.8d+41) then
        tmp = (x / z) - x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+17) {
		tmp = y / (z / x);
	} else if (y <= 4.8e+41) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e+17:
		tmp = y / (z / x)
	elif y <= 4.8e+41:
		tmp = (x / z) - x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e+17)
		tmp = Float64(y / Float64(z / x));
	elseif (y <= 4.8e+41)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e+17)
		tmp = y / (z / x);
	elseif (y <= 4.8e+41)
		tmp = (x / z) - x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e+17], N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+41], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e17

   1. Initial program 90.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in y around inf 77.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   3. Step-by-step derivation

      1. associate-/l* 68.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

      2. associate-/r/ 73.0%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   4. Simplified 73.0%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]
   5. Step-by-step derivation

      1. *-commutative 73.0%

         \[\leadsto \color{blue}{y \cdot \frac{x}{z}} \]

      2. clear-num 73.0%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{z}{x}}} \]

      3. un-div-inv 73.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]

   6. Applied egg-rr 73.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}} \]

   if -8e17 < y < 4.8000000000000003e41

   1. Initial program 91.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around 0 96.6%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x}{z}} \]
   4. Step-by-step derivation

      1. neg-mul-1 96.6%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \]

      2. +-commutative 96.6%

         \[\leadsto \color{blue}{\frac{x}{z} + \left(-x\right)} \]

      3. unsub-neg 96.6%

         \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   5. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   if 4.8000000000000003e41 < y

   1. Initial program 90.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in y around inf 80.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   3. Step-by-step derivation

      1. associate-/l* 79.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

      2. associate-/r/ 84.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   4. Simplified 84.8%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+17}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+41}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 14: 85.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.1e+17)
   (/ (* x y) z)
   (if (<= y 2.6e+40) (- (/ x z) x) (* y (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.1e+17) {
		tmp = (x * y) / z;
	} else if (y <= 2.6e+40) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.1d+17)) then
        tmp = (x * y) / z
    else if (y <= 2.6d+40) then
        tmp = (x / z) - x
    else
        tmp = y * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.1e+17) {
		tmp = (x * y) / z;
	} else if (y <= 2.6e+40) {
		tmp = (x / z) - x;
	} else {
		tmp = y * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.1e+17:
		tmp = (x * y) / z
	elif y <= 2.6e+40:
		tmp = (x / z) - x
	else:
		tmp = y * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.1e+17)
		tmp = Float64(Float64(x * y) / z);
	elseif (y <= 2.6e+40)
		tmp = Float64(Float64(x / z) - x);
	else
		tmp = Float64(y * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.1e+17)
		tmp = (x * y) / z;
	elseif (y <= 2.6e+40)
		tmp = (x / z) - x;
	else
		tmp = y * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.1e+17], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.6e+40], N[(N[(x / z), $MachinePrecision] - x), $MachinePrecision], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.1e17

   1. Initial program 90.3%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in y around inf 77.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]

   if -5.1e17 < y < 2.6000000000000001e40

   1. Initial program 91.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x \cdot \left(1 + y\right)}{z}} \]

   3. Taylor expanded in y around 0 96.6%

      \[\leadsto \color{blue}{-1 \cdot x + \frac{x}{z}} \]
   4. Step-by-step derivation

      1. neg-mul-1 96.6%

         \[\leadsto \color{blue}{\left(-x\right)} + \frac{x}{z} \]

      2. +-commutative 96.6%

         \[\leadsto \color{blue}{\frac{x}{z} + \left(-x\right)} \]

      3. unsub-neg 96.6%

         \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   5. Simplified 96.6%

      \[\leadsto \color{blue}{\frac{x}{z} - x} \]

   if 2.6000000000000001e40 < y

   1. Initial program 90.6%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in y around inf 80.4%

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}} \]
   3. Step-by-step derivation

      1. associate-/l* 79.4%

         \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}} \]

      2. associate-/r/ 84.8%

         \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]

   4. Simplified 84.8%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z} - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 15: 64.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0) (- x) (if (<= z 6e+17) (/ x z) (- x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 6e+17) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.0d0)) then
        tmp = -x
    else if (z <= 6d+17) then
        tmp = x / z
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = -x;
	} else if (z <= 6e+17) {
		tmp = x / z;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.0:
		tmp = -x
	elif z <= 6e+17:
		tmp = x / z
	else:
		tmp = -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.0)
		tmp = Float64(-x);
	elseif (z <= 6e+17)
		tmp = Float64(x / z);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.0)
		tmp = -x;
	elseif (z <= 6e+17)
		tmp = x / z;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.0], (-x), If[LessEqual[z, 6e+17], N[(x / z), $MachinePrecision], (-x)]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 6e17 < z

   1. Initial program 80.5%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

   2. Taylor expanded in z around inf 73.5%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. neg-mul-1 73.5%

         \[\leadsto \color{blue}{-x} \]

   4. Simplified 73.5%

      \[\leadsto \color{blue}{-x} \]

   if -1 < z < 6e17

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]
   2. Step-by-step derivation

      1. distribute-lft-in 99.9%

         \[\leadsto \frac{\color{blue}{x \cdot \left(y - z\right) + x \cdot 1}}{z} \]

      2. fma-def 99.9%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x, y - z, x \cdot 1\right)}}{z} \]

      3. *-rgt-identity 99.9%

         \[\leadsto \frac{\mathsf{fma}\left(x, y - z, \color{blue}{x}\right)}{z} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, y - z, x\right)}{z}} \]

   4. Taylor expanded in z around 0 97.6%

      \[\leadsto \color{blue}{\frac{x + x \cdot y}{z}} \]

   5. Taylor expanded in x around -inf 97.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot \left(-1 \cdot y - 1\right)}{z}} \]
   6. Step-by-step derivation

      1. mul-1-neg 97.6%

         \[\leadsto \color{blue}{-\frac{x \cdot \left(-1 \cdot y - 1\right)}{z}} \]

      2. associate-/l* 88.8%

         \[\leadsto -\color{blue}{\frac{x}{\frac{z}{-1 \cdot y - 1}}} \]

      3. distribute-neg-frac 88.8%

         \[\leadsto \color{blue}{\frac{-x}{\frac{z}{-1 \cdot y - 1}}} \]

      4. sub-neg 88.8%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{-1 \cdot y + \left(-1\right)}}} \]

      5. neg-mul-1 88.8%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{\left(-y\right)} + \left(-1\right)}} \]

      6. metadata-eval 88.8%

         \[\leadsto \frac{-x}{\frac{z}{\left(-y\right) + \color{blue}{-1}}} \]

      7. +-commutative 88.8%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{-1 + \left(-y\right)}}} \]

      8. unsub-neg 88.8%

         \[\leadsto \frac{-x}{\frac{z}{\color{blue}{-1 - y}}} \]

   7. Simplified 88.8%

      \[\leadsto \color{blue}{\frac{-x}{\frac{z}{-1 - y}}} \]

   8. Taylor expanded in y around 0 53.0%

      \[\leadsto \color{blue}{\frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;-x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 16: 39.0% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x))

C

double code(double x, double y, double z) {
	return -x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -x
end function

Java

public static double code(double x, double y, double z) {
	return -x;
}

Python

def code(x, y, z):
	return -x

Julia

function code(x, y, z)
	return Float64(-x)
end

MATLAB

function tmp = code(x, y, z)
	tmp = -x;
end

Wolfram

code[x_, y_, z_] := (-x)

Derivation

1. Initial program 91.0%

   \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \]

2. Taylor expanded in z around inf 35.3%

   \[\leadsto \color{blue}{-1 \cdot x} \]
3. Step-by-step derivation

   1. neg-mul-1 35.3%

      \[\leadsto \color{blue}{-x} \]

4. Simplified 35.3%

   \[\leadsto \color{blue}{-x} \]

5. Final simplification 35.3%

   \[\leadsto -x \]

Developer target: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* (+ 1.0 y) (/ x z)) x)))
   (if (< x -2.71483106713436e-162)
     t_0
     (if (< x 3.874108816439546e-197)
       (* (* x (+ (- y z) 1.0)) (/ 1.0 z))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 + y) * (x / z)) - x
    if (x < (-2.71483106713436d-162)) then
        tmp = t_0
    else if (x < 3.874108816439546d-197) then
        tmp = (x * ((y - z) + 1.0d0)) * (1.0d0 / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((1.0 + y) * (x / z)) - x;
	double tmp;
	if (x < -2.71483106713436e-162) {
		tmp = t_0;
	} else if (x < 3.874108816439546e-197) {
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((1.0 + y) * (x / z)) - x
	tmp = 0
	if x < -2.71483106713436e-162:
		tmp = t_0
	elif x < 3.874108816439546e-197:
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(1.0 + y) * Float64(x / z)) - x)
	tmp = 0.0
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = Float64(Float64(x * Float64(Float64(y - z) + 1.0)) * Float64(1.0 / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((1.0 + y) * (x / z)) - x;
	tmp = 0.0;
	if (x < -2.71483106713436e-162)
		tmp = t_0;
	elseif (x < 3.874108816439546e-197)
		tmp = (x * ((y - z) + 1.0)) * (1.0 / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(1.0 + y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]}, If[Less[x, -2.71483106713436e-162], t$95$0, If[Less[x, 3.874108816439546e-197], N[(N[(x * N[(N[(y - z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))